Poincare-Hopf relationship

In an isolated molecule, or cluster of atoms, the Poincare-Hopf relationship... 

The number and type of critical points which can coe dst in a system with a finite number of nuclei are governed by the Poincare-Hopf relationship. With the above association of each type of critical point with an element of... 

To apply QTAIM, one first determines the molecular graph. The molecular graph of phenanthrene [48] exhibits a H-H bond path between the two nuclei of H4 and H5 which are separated by 2.03 A. The formation of the H-H bond in phenanthrene closes a 6-membered ring (6-MR) and is accompanied by the appearance of a ring critical point (RCP), as required for the satisfaction of the Poincare-Hopf relationship [63]. In contrast, there are no H-H bond paths in phenanthrene s isomer anthracene (see the comparison of the molecular graphs in Fig. 3). 

Electrostatic Potential. - An investigation of the topology of the MEP led to a chemical interpretation of the CPS in terms of lone pairs, n bonds, hybrid orbitals and other electronic structure elements. A Poincare-Hopf relationship for the MEP connects electronic structure elements and electrostatic reactivity. 

The same topology is observed at any distance for the three systems a (3, -1) CP is present between the two moieties. This is actually expected from the Poincare-Hopf (PH) relationship, as derived in Ref. [105]. Indeed, the two fragments keep... 

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